Method and system for creating a volatility benchmark index

ABSTRACT

A method and system for creating a volatility benchmark index is disclosed. The method includes obtaining a value of a Treasury bill account less a mark-to-market value of at least one of a volatility-based future or option and calculating a value reflecting a volatility benchmark. The value may be displayed at a trading facility and volatility benchmark quotes may be transmitted by the trading facility to a market participant.

RELATED APPLICATIONS

The present application claims the benefit of U.S. Patent ApplicationSer. No. 60/986,718 filed Nov. 9, 2007, the entirety of which is herebyincorporated by reference.

TECHNICAL FIELD

The present invention relates generally to financial trading systems andmore particularly to the generation, identification, processing,trading, quotation, and valuation of volatility benchmark indices andrelated derivative investment instruments.

BACKGROUND

An index is a statistical composite that is used to indicate theperformance of a market or a market sector over various time periods.Examples of indices that are used to gauge the performance of stocks andother securities in the United States include the Dow Jones IndustrialAverage, the National Association of Securities Dealers AutomatedQuotations (NASDAQ) Composite Index, the New York Stock ExchangeComposite Index, etc. In general, the Dow Jones Industrial Averagecontains thirty (30) stocks that trade on the New York Stock Exchange aswell as NASDAQ, and is a general indicator of how shares of the largestUnited States companies are trading. The NASDAQ Composite Index is acomposite index of more than three thousand (3,000) companies listed onthe NASDAQ (also referred to as over-the-counter or OTC stocks). It isdesigned to indicate the stock performance of small-cap and technologystocks. Finally, the New York Stock Exchange Composite Index is acomposite index of shares listed on the New York Stock Exchange.

In equal-dollar weighted indices, the weights of each component arereset to equal values at regular intervals, such as for example, everyquarter. Between re-adjustments, the weights of the various indexcomponents will deviate from the equal-dollar weighting values as thevalues of the components fluctuate. Periodically, indices must beadjusted in order to reflect changes in the component companiescomprising the index, or to maintain the original intent of the index inview of changing conditions in the market. For example, if a componentstock's weight drops below an arbitrary threshold, or if a componentcompany significantly alters its line of business or is taken over byanother company so that it no longer represents the type of companywhich the index is intended to track, the index may no longer beinfluenced by, or reflect the aspects of the market for which it wasoriginally designed. In such cases it may be necessary to replace acomponent stock with a suitable replacement stock. If a suitablereplacement that preserves the basic character of the index cannot befound, the stock may simply be dropped without adding a replacement.Conversely, activity in the market for which an index is created maydictate that a new stock (which was not originally included in theindex) having a strong impact in the market be added to the index toadequately reflect the market without eliminating other components. Ineach case, the divisor may be adjusted so that the index remains at thesame level immediately after the new stock is added or the old stock iseliminated.

Derivatives are financial securities whose values are derived in partfrom a value or characteristic of some other underlying asset orvariable (the underlying asset). The underlying asset may includesecurities such as stocks, market indicators and indices, interest rate,and corporate debt, such as bonds, to name but a few. Two common formsof derivatives are options contracts and futures contracts, discussedherein below.

An option is a contract giving the holder of the option the right, butnot the obligation, to buy or sell an underlying asset at a specificprice on or before a certain date. Generally, a party who purchases anoption is said to have taken a long position with respect to the option.The party who sells the option is said to have taken a short position.There are generally two types of options: calls and puts. An investorwho has taken a long position in a call option has bought the right topurchase the underlying asset at a specific price, known as the “strikeprice.” If the long investor chooses to exercise the call option, thelong investor pays the strike price to the short investor, and the shortinvestor is obligated to deliver the underlying asset.

Alternatively, an investor who has taken a long position in a put optionreceives the right, but not the obligation to sell the underlying assetat a specified price, again referred to as the strike price on or beforea specified date. If the long investor chooses to exercise the putoption, the short investor is obligated to purchase the underlying assetfrom the long investor at the agreed upon strike price. The longinvestor must then deliver the underlying asset to the short investor.Thus, the traditional settlement process for option contracts involvesthe transfer of funds from the purchaser of the underlying asset to theseller, and the transfer of the underlying asset from the seller of theunderlying asset to the purchaser. Cash settlement, however, is morecommon. Cash settlement allows options contracts to be settled withoutactually transferring the underlying asset.

A call option is “in-the-money” when the price or value of theunderlying asset rises above the strike price of the option. A putoption is “in-the-money” when the price or value of the underlying assetfalls below the strike price of the option. An at-the-money optionwherein the price or value of the underlying asset is equal to thestrike price of the option. A call option is out-of-the-money when theprice or value of the underlying asset is below the strike price. A putoption is out-of-the-money when the price or value of the underlyingasset is above the strike price. If an option expires at-the-money orout-of-the-money, it has no value. The short investor retains the amountpaid by the long investor (the option price) and pays nothing to thelong investor. Cash settlement of an in-the-money option, be it a callor a put, however, requires the short investor to pay to the longinvestor the difference between the strike price and the current marketvalue of the underlying asset.

Cash settlement allows options to be based on more abstract underlying“assets” such as market indicators, stock indices, interest rates,futures contracts and other derivatives. For example, an investor maytake a long position in a market index call option. In this case, thelong investor receives the right to “purchase” not the index itself, butrather a cash amount equal to the value of the index (typicallymultiplied by a multiplier) at a specified strike value. An index calloption is in-the-money when the value of the index rises above thestrike value. When the holder of an in-the-money index call optionexercises the option, the short investor on the opposite side of thecontract is obligated to pay the long investor the difference betweenthe current value of the index and the strike price, usually multipliedby the multiplier. If the current value of the index is less than orequal to the strike value, the option has no value. An index put optionworks in the same way but in reverse, having value, or beingin-the-money when the value of the index falls below the strike value.

Futures contracts are another common derivative security. In a futurescontract a buyer purchases the right to receive delivery of anunderlying commodity or asset on a specified date in the future.Conversely, a seller agrees to deliver the commodity or asset to anagreed location on the specified date. Futures contracts originallydeveloped in the trade of agricultural commodities, but quickly spreadto other commodities as well. Because futures contracts establish aprice for the underlying commodity in advance of the date on which thecommodity must be delivered, subsequent changes in the price of theunderlying asset will inure to the benefit of one party and to thedetriment of the other. If the price rises above the futures price, theseller is obligated to deliver the commodity at the lower agreed uponprice. The buyer may then resell the received product at the highermarket price to realize a profit. The seller in effect loses thedifference between the futures contract price and the market price onthe date the goods are delivered. Conversely if the price of theunderlying commodity falls below the futures price, the seller canobtain the commodity at the lower market price for delivery to the buyerwhile retaining the higher futures price. In this case the sellerrealizes a profit in the amount of the difference between the currentmarket price on the delivery date and the futures contract price. Thebuyer sees an equivalent loss. Like options contracts, futures contractsmay be settled in cash. Rather than actually delivering the underlyingasset, cash settlement merely requires payment of the difference betweenthe market price of the underlying commodity or asset on the deliverydate and the futures contract price. The difference between the marketprice and the futures price is to be paid by the short investor to thelong investor, or by the long investor to the short investor, dependingon which direction the market price has moved. If the prevailing marketprice is higher than the contract price, the short investor must pay thedifference to the long investor. If the market price has fallen, thelong investor must pay the difference to the short investor.

Again, like options, cash settlement allows futures contracts to bewritten against more abstract underlying “assets” or “commodities,” suchas market indicators, stock indices, interest rates, futures contractsand other derivatives. For example, an investor may take a long positionin a market index futures contract. In this case, the long investor“buys” the index at a specified futures price (i.e. a future value ofthe index on the “delivery” date). The index based futures contract iscash settled. One party to the contract pays the difference between thefutures price and the actual value of the index (often multiplied by aspecified multiplier) to the other investor depending on which directionthe market has moved. If the value of the index has moved above thefutures price, or futures value, the short investor pays the differencethe long investor. If the value of the index has moved below the futuresprice, or futures value the long investor pays the difference to theshort investor.

The Chicago Board Options Exchange (OBOE) introduced the OBOE VolatilityIndex®, VIX®, which quickly became the benchmark for stock marketvolatility. The VIX methodology was subsequently updated to ensure thatVIX remains the premier benchmark of U.S. stock market volatility, asdescribed in co-pending U.S. patent application Ser. No. 10/959,928, theentirety of which is hereby incorporated by reference.

Cash settlement provides great flexibility regarding the types ofunderlying assets that derivative investment instruments may be builtaround.

BRIEF SUMMARY

In order to provide for improvements on indices and derivativeinvestment instruments, volatility benchmark index derivative investmentinstruments and methods for creating a volatility benchmark index aredisclosed herein based on changes in the performance of periodicallyselling a volatility-based derivatives contract.

According to a first aspect of the disclosure, a method for creating avolatility benchmark index is provided. The method medium may includethe steps of obtaining a value of a Treasury bill account less amark-to-market value of at least one of a volatility-based future oroption and calculating a value reflecting a volatility benchmark. Thevalue reflecting a volatility benchmark is calculated according to theformula:

VPD _(t) =M _(t)=(1+r _(t−1))VPD _(t−1)−M_(ult) N _(last)(f _(t) −f_(t−1))

where VPD_(t) is the VIX premium index value at date t, M_(t) is aTreasury bill balance on date t, r_(t−1) is the effective Treasury billrate from date t−1 to date t, N_(last) is a number of futures sold at alast roll date, F_(t) is a daily settlement price of futures t, andM_(ult) is a multiplier of the futures A computer readable mediumcontaining processor executable instructions for executing the abovemethod is also contemplated, as is a trading system incorporating thevolatility benchmark calculation set forth above.

BRIEF DESCRIPTION OF THE DRAWINGS

For the purpose of facilitating an understanding of the subject mattersought to be protected, there is illustrated in the accompanyingdrawings an embodiment thereof, from an inspection of which, whenconsidered in connection with the following description, the subjectmatter sought to be protected, its construction and operation, and manyof its advantages should be readily understood and appreciated.

FIG. 1 is a graph illustrating one embodiment of an example volatilitybenchmark index that calculates a value of performance of periodicallyselling a volatility-based derivative investment instrument.

FIG. 2 is a graph illustrating a frequency of monthly returns based onthe volatility benchmark index of FIG. 1.

FIG. 3 is a block diagram of a system for creating and tradingderivative investment instruments based on a volatility benchmark index.

FIG. 4 a general computer system that may be used for one or more of thecomponents shown in FIG. 3.

DETAILED DESCRIPTION

The steady growth of Chicago Board Option Exchange's (CBOE's) volatilitycomplex provides a unique opportunity for investors intent on capturingthe “volatility premium.” The volatility premium is the risk premiumthat the market seems willing to pay to own realized or impliedvolatility. The prevalent conjecture among financial economists is thatthe volatility premium is explained by the negative correlation betweenS&P 500 volatility and S&P 500 returns. The volatility premium hasalways been reflected in the difference between implied and realizedvolatility, and it now has become apparent in the historical returns ofshort positions in VIX and variance futures.

To benchmark the returns of short volatility strategies, OBOE hasdeveloped two different benchmarks, S&P 500 VARB-X, an index based onselling three-month realized variance futures, and the VIX PremiumIndex, based on selling VIX futures. To clarify the differences betweenthe two indexes, recall that December 2007 VIX futures settle to thevalue of VIX on Dec. 19, 2007 while December 2007 three-month variancefutures settle to the realized variance of the S&P 500 in thethree-months that precede Dec. 21, 2007, when the variance futuresexpire. The VARB-X Index is thus short 3-month spot realized variancewhile the VIX Premium Index is short forward one-month impliedvolatility. A second and related difference is that the exposure of theVARB-X Index to volatility risk gradually decreases as each day revealsanother term of the final realized variance. In contrast to this, theexposure of the VIX Premium Index to volatility is constant as VIXfutures approach maturity. The VIX Premium Index is also inherently morevolatile than the VARB-X Index. The VIX Premium Index therefore offers adifferent take on the volatility premium that more capitalized and/orless risk averse investors may like.

This index tracks the value of a portfolio that overlays a sequence ofshort one-month VIX futures on a money market account. The VIX futuresare held until expiration and new VIX futures are then sold. The moneymarket account decreases leverage relative to a stand-alone shortposition in VIX futures. To further limit risk, the number of VIXfutures sold at each roll is set to preserve 75% of the initial value ofthe portfolio in the event that VIX futures increase by 25 points. Thedecision to target the maximum loss resulting from a 25 point increasein VIX futures is based on the historical frequency distribution ofone-month changes in implied volatility, as proxied by VXO, a priorversion of VIX. Over any one-month period between January 1986 and July2007, VXO has increased by more than 25 points 0.34% of the time, and0.037% if we omit the fall of 1987. In a second version of the index,the short VIX futures position is capped with long VIX calls struck 25points higher than the VIX futures price, or calls at the closest strikebelow if this strike is not listed.

Historical Performance

Applying the present method to historical data ranging from June 2004 toOctober 2007, the VIX Premium Index increased by approximately 60% andearned an annual geometric return of 18.29% (17.68% when capped). Overthe same period, the S&P 500 Total Return Index (SPTR) increased byapproximately 43% and earned an annual geometric return of 12.67%. FIGS.1 and 2 illustrate these returns using data from the June 2004 throughOctober 2007 time period. The pronounced skew of the VIX Premium Indexreturn suggests that the semi-standard deviation is a better proxy forrisk than the standard deviation. As shown in Table 1 below, thesemi-standard deviation of the VIX Premium Index was 6.64% (6.70% whencapping the index), slightly smaller than the 8.16% deviation of the S&P500. Adjusting its monthly rate of return for risk, the VIX Premiumperformed better than the S&P 500.

TABLE 1 VIX Premium VIX Monthly Returns 25% loss at 25 Premium 3/04-7/07SPTR VARB-X pt vol increase Capped Minimum Return −3.93% −4.25% −4.34%Arithmetic Mean  1.03%  1.44%  1.40% Monthly Annualized Std.  8.16% 6.64%  6.70% Deviation Annualized 12.67% 18.29% 17.69% Geometric MeanMonthly Sharpe 0.31   0.59    0.56   Ratio Monthly Semi- 0.14   0.20   0.19   Sharpe Ratio Skew −0.20   −0.77    −0.76  

Construction of VIX Premium Capped Index

The VIX Premium Index represents the value of an initial investment of$100 in a portfolio that passively follows the VIX Premium cappedstrategy. The uncapped strategy is identical except that no calls arebought. The portfolio may be managed and calculated as in the followingexample:

At the close of June 15, 2006, the inception date, $100 is invested atthe three-month Treasury bill rate. The intra-day cash from settlingfutures at the open is deemed to be invested at the close of the rolldate. Similarly, settlement losses are deemed to be financed at theclose. On June 16, 2007, the first roll date, VIX futures are sold atthe opening bid price of VIX futures and an equal number of VIX callsare bought at a strike price 25 points greater than the opening bidprice of VIX futures. If this strike price is not listed, the calls arebought at the closest strike below. From thereon, the futures andoptions are marked-to-market daily at the close and the resulting cashflow is credited to or debited from the opening money market balance.

At the next expiration, the futures and option positions are settled atthe open to their final settlement price, new VIX futures are sold atthe opening bid price and new VIX calls are bought at the opening askprice. The cash flows from the final mark of expiring contracts and fromthe daily closing marks of the new contracts are financed from the moneymarket balance.

This process is repeated from expiration to expiration. During the firsttwo years of VIX futures, new contracts expiring in the next month werenot listed on several occasions. The index was then calculated using aposition in the second month.

Final Settlement Price of Expiring VIX Futures

At expiration, VIX futures and options are settled to a Special OpeningQuotation of VIX. The SOQ is a special calculation of VIX compiled fromthe opening prices of 500 options.

Example Index Calculation 1 VIX Premium Index

CBOE's proposed index calculation will calculate VIX Premium Index onceper day at the close of trading. On any given date, the index representsthe mark-to-market value of the initial $100 invested in the VIX PremiumStrategy.

At the close of every business date, the value of the VIX Premium Indexis equal to the value of the Treasury bill account less themark-to-market value of the VIX futures and calls:

VPI _(t) =M _(t)−1000 N _(last)(F _(t) −F _(t−1))+1000 N _(last)(C _(t)−C _(t−1))

where M_(t) is the Treasury bill balance on date t, N_(last) is thenumber of futures sold and options bought at the last roll date, F_(t)is the daily settlement price of VIX futures t, and C_(t) is the averageof the bid and ask prices of VIX calls on date t. 1000 is the multiplierof VIX future and 100 the multiplier of VIX options.

The Treasury bill balance is obtained by compounding the previousclosing balance at the three-month Treasury bill rate:

M _(t)=(1+r _(t−1))VPI _(t−1)

where r_(t−1) is the effective Treasury bill rate from date t−1 to datet.

On a roll date,

VPI _(t) =M _(t)−1000(N _(last)(SOQ _(t) −F _(t−1) ]−N _(new)(F _(t) −F_(bid) ^(o)))+100(N _(last)Max(0,SOQ _(t) −K)+N _(new)(C _(t) −C _(ask)^(o)))

where SOQ_(t) is the final settlement price of the expiring VIX futures,N_(new) is the number of new VIX futures sold and VIX calls bought,F_(bid) ^(o) is the opening bid price of VIX futures and C_(ask) ^(o) isthe opening ask price of VIX calls. This balance is reinvested at theTreasury rate.

The number of new VIX futures sold and VIX calls bought on any roll datet is set such that a 25 point increase of VIX futures at the next rollstill preserves 75% of initial capital.

N_(new) =M _(t)(1+R _(t)−0.75)/(1000*(25+(1+R _(t))C _(ask) ^(o))

where R_(t) is the effective three-month Treasury bill rate to the nextroll date.

Example Calculation 2 VIX Premium Benchmark Index (VPD)

At the close of every business date, the value of the Volatility PremiumIndex is equal to the value of the Treasury bill account, obtained bycompounding the Treasury bill balance at the previous close by theTreasury rate and netting the cash flow from marking VIX futures tomarket:

VPD _(t) =M _(t)=(1+r _(t−1))VPD _(t−1) −M _(ult) N _(last)(F _(t) −F_(t−1))

where M_(t) is the Treasury bill balance at the close of date t, r_(t−1)is the effective Treasury bill rate from date t−1 to date t, N_(last) isthe number of futures sold at the last roll date, F_(t) is the dailysettlement price of VIX futures t, and M_(ult) is the multiplier of VIXfutures (for example, 1000).

On a roll date, the cash flow from final settlement of the expiringfutures and their daily mark at the close are both netted from the moneymarket balance:

VPD _(t)=(1+r _(t−1))VPD _(t−1) −M _(ult)(SOQ _(t) −F _(t−1))−N _(new)(F_(t) −F _(bid)))

where SOQ_(t) is the final settlement price of the expiring VIX futures,N_(new) is the number of new VIX futures sold, and F_(bid) is theopening bid price of VIX futures. This balance is reinvested at thedaily Treasury rate until the next date.

The number of new VIX futures sold at the open on a roll date t is setsuch that a 25 point increase of VIX futures at the next roll stillpreserves 75% of capital available after the final settlement of VIXfutures:

N _(new) =M _(t) ^(o)(1+R _(t)−0.75)/(1000*25)

where M_(t) ^(o) is the amount in the money market account at the openafter the final settlement of VIX futures, and R_(t) is the effectivethree-month Treasury bill rate to the next roll date.

M _(t) ^(o) =M _(t−1) −M _(ult) N _(last)(SOQ_(t) −F _(t−1))

Example Calculation 3 Capped VIX Premium Benchmark Index (VPN)

At the close of every business date, the value of the VPD is equal tothe closing value of the Treasury bill account plus the mark-to-marketvalue of the VIX calls:

VPD _(t) =M _(t)+100*10 N _(last) C _(t)

where M_(t) is the Treasury bill balance at the close of date t,N_(last) is the number of futures sold and 10 N_(last) is the number ofVIX options bought at the last roll date, F_(t) is the daily settlementprice of VIX futures t, and C_(t) is the average of the bid and askquotes of the VIX calls at the close. The Treasury bill balance isobtained by compounding the previous closing Treasury balance at thethree-month Treasury bill rate and netting the cash flow from the markof VIX futures:

M _(t)=(1+r _(t−1))M _(t−1) −M _(ult) N _(last)(F _(t) −F _(t−1))

M _(t−1) =VPD _(t−1) −M _(ult) N _(last) C _(t)

where r_(t−1) is the effective Treasury bill rate from date t−1 to datet.

At the close of a roll date, as on regular days, the index is equal tothe closing Treasury balance plus the mark of the new options. Theclosing Treasury balance is now equal to the Treasury balance at theprevious close compounded by the daily Treasury rate net of the cashflows from (1) final settlements of VIX futures and options, (2) thedaily mark of new VIX futures and (3) the purchase of new VIX calls.

VPD _(t)=(1+r _(t−1))M _(t−1) +M _(ult) N _(last)(max[0,SOQ _(t)−K]−(SOQ _(t) −F _(t−1)))+M _(ult) N _(new)(C _(t) −C _(a)−(F _(t) −F_(bid)))

where SOQ_(t) is the final settlement price of the expiring VIX futures,K is the strike of the expiring VIX calls, N_(new) is the number of newVIX futures sold, C^(a) is the ask price of the VIX calls bought at theopen, F_(bid) is the opening bid price of VIX futures. As on non-rolldates, the Treasury balance is reinvested at the Treasury rate.

The number of new VIX futures sold on a roll date t is set such that a25 point increase of VIX futures at the next roll still preserves 75% ofcapital available after the final settlement of the VIX futures andoptions:

N _(new) =M _(t) ^(o)(1+R _(t)−0.75)/(1000*(25+(1+R _(t))C _(ask))

M _(t) ^(o)=(1+r _(t−1))M _(t−1) +M _(ult) N _(last)(max[0,SOQ _(t)−K]−(SOQ _(t) −F _(t−1)))

where R_(t) is the effective three-month Treasury bill rate to the nextroll date.

FIG. 3 is a block diagram of a system 200 for creating and tradingderivative investment instruments based on a volatility benchmark index.Generally, the system comprises a volatility benchmark index module 202,a dissemination module 204 coupled with the volatility benchmark indexmodule 202, and a trading module 206 coupled with the disseminationmodule 204. Typically, each module 202, 204, 206 is also coupled to acommunication network 208 coupled to various trading facilities 222 andliquidity providers 224.

The volatility benchmark index module 202 comprises a communicationsinterface 210, a processor 212 coupled with the communications interface210, and a memory 214 coupled with the processor 212. Logic stored inthe memory 214 is executed by the processor 212 such that that thevolatility benchmark index module 202 may receive a first set of tradeinformation for each underlying asset representative of a desired groupof underlying assets through the communications interface 210, aggregatethat first set of trade information over a first time period, calculatea volatility benchmark index for the desired group of underlying assetswith the aggregated first set of trade information, and a standardizedmeasure of the index; and pass the calculated values to thedissemination module 204.

The dissemination module 204 comprises a communications interface 216, aprocessor 218 coupled with the communications interface 216, and amemory 220 coupled with the processor 218. Logic stored in the memory220 is executed by the processor 218 such that the dissemination module204 may receive the calculated values from the volatility benchmarkindex module 202 through the communications interface 216, anddisseminate the calculated values over the communications network 208 tovarious market participants 222.

The trading module 206 comprises a communications interface 226, aprocessor 228 coupled with the communications interface 226, and amemory 230 coupled with the processor 228. Logic stored in the memory230 is executed by the processor 228 such that the trading module 206may receive buy or sell orders over the communications network 208, asdescribed above, and pass the results of the buy or sell order to thedissemination module 204 to be disseminated over the communicationsnetwork 208 to the market participants 222.

Referring to FIG. 4, an illustrative embodiment of a general computersystem that may be used for one or more of the components shown in FIG.3, or in any other trading system configured to carry out the methodsdiscussed above, is shown and is designated 300. The computer system 300can include a set of instructions that can be executed to cause thecomputer system 300 to perform any one or more of the methods orcomputer based functions disclosed herein. The computer system 300 mayoperate as a standalone device or may be connected, e.g., using anetwork, to other computer systems or peripheral devices.

In a networked deployment, the computer system may operate in thecapacity of a server or as a client user computer in a server-clientuser network environment, or as a peer computer system in a peer-to-peer(or distributed) network environment. The computer system 300 can alsobe implemented as or incorporated into various devices, such as apersonal computer (PC), a tablet PC, a set-top box (STB), a personaldigital assistant (PDA), a mobile device, a palmtop computer, a laptopcomputer, a desktop computer, a network router, switch or bridge, or anyother machine capable of executing a set of instructions (sequential orotherwise) that specify actions to be taken by that machine. In aparticular embodiment, the computer system 300 can be implemented usingelectronic devices that provide voice, video or data communication.Further, while a single computer system 300 is illustrated, the term“system” shall also be taken to include any collection of systems orsub-systems that individually or jointly execute a set, or multiplesets, of instructions to perform one or more computer functions.

As illustrated in FIG. 4, the computer system 300 may include aprocessor 302, e.g., a central processing unit (CPU), a graphicsprocessing unit (GPU), or both. Moreover, the computer system 300 caninclude a main memory 304 and a static memory 306 that can communicatewith each other via a bus 308. As shown, the computer system 300 mayfurther include a video display unit 310, such as a liquid crystaldisplay (LCD), an organic light emitting diode (OLED), a flat paneldisplay, a solid state display, or a cathode ray tube (CRT).Additionally, the computer system 300 may include an input device 312,such as a keyboard, and a cursor control device 314, such as a mouse.The computer system 300 can also include a disk drive unit 316, a signalgeneration device 318, such as a speaker or remote control, and anetwork interface device 320.

In a particular embodiment, as depicted in FIG. 4, the disk drive unit316 may include a computer-readable medium 322 in which one or more setsof instructions 324, e.g. software, can be embedded. Further, theinstructions 324 may embody one or more of the methods or logic asdescribed herein. In a particular embodiment, the instructions 324 mayreside completely, or at least partially, within the main memory 304,the static memory 306, and/or within the processor 302 during executionby the computer system 300. The main memory 304 and the processor 302also may include computer-readable media.

In an alternative embodiment, dedicated hardware implementations, suchas application specific integrated circuits, programmable logic arraysand other hardware devices, can be constructed to implement one or moreof the methods described herein. Applications that may include theapparatus and systems of various embodiments can broadly include avariety of electronic and computer systems. One or more embodimentsdescribed herein may implement functions using two or more specificinterconnected hardware modules or devices with related control and datasignals that can be communicated between and through the modules, or asportions of an application-specific integrated circuit. Accordingly, thepresent system encompasses software, firmware, and hardwareimplementations.

In accordance with various embodiments of the present disclosure, themethods described herein may be implemented by software programsexecutable by a computer system. Further, in an exemplary, non-limitedembodiment, implementations can include distributed processing,component/object distributed processing, and parallel processing.Alternatively, virtual computer system processing can be constructed toimplement one or more of the methods or functionality as describedherein.

The present disclosure contemplates a computer-readable medium thatincludes instructions 324 or receives and executes instructions 324responsive to a propagated signal, so that a device connected to anetwork 326 can communicate voice, video or data over the network 326.Further, the instructions 324 may be transmitted or received over thenetwork 326 via the network interface device 320.

While the computer-readable medium is shown to be a single medium, theterm “computer-readable medium” includes a single medium or multiplemedia, such as a centralized or distributed database, and/or associatedcaches and servers that store one or more sets of instructions. The term“computer-readable medium” shall also include any medium that is capableof storing, encoding or carrying a set of instructions for execution bya processor or that cause a computer system to perform any one or moreof the methods or operations disclosed herein.

In a particular non-limiting, exemplary embodiment, thecomputer-readable medium can include a solid-state memory such as amemory card or other package that houses one or more non-volatileread-only memories. Further, the computer-readable medium can be arandom access memory or other volatile re-writable memory. Additionally,the computer-readable medium can include a magneto-optical or opticalmedium, such as a disk or tapes or other storage device to capturecarrier wave signals such as a signal communicated over a transmissionmedium. A digital file attachment to an e-mail or other self-containedinformation archive or set of archives may be considered a distributionmedium that is equivalent to a tangible storage medium. Accordingly, thedisclosure is considered to include any one or more of acomputer-readable medium or a distribution medium and other equivalentsand successor media, in which data or instructions may be stored.

Although the present specification describes components and functionsthat may be implemented in particular embodiments with reference toparticular standards and protocols commonly used on financial exchanges,the invention is not limited to such standards and protocols. Forexample, standards for Internet and other packet switched networktransmission (e.g., TCP/IP, UDP/IP, HTML, HTTP) represent examples ofthe state of the art. Such standards are periodically superseded byfaster or more efficient equivalents having essentially the samefunctions. Accordingly, replacement standards and protocols having thesame or similar functions as those disclosed herein are consideredequivalents thereof.

One or more embodiments of the disclosure may be referred to herein,individually and/or collectively, by the term “invention” merely forconvenience and without intending to voluntarily limit the scope of thisapplication to any particular invention or inventive concept. Moreover,although specific embodiments have been illustrated and describedherein, it should be appreciated that any subsequent arrangementdesigned to achieve the same or similar purpose may be substituted forthe specific embodiments shown. This disclosure is intended to cover anyand all subsequent adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, will be apparent to those of skill in theart upon reviewing the description.

As will be appreciated by those of ordinary skill in the art, mechanismsfor creating a volatility benchmark index, derivative investmentinstruments based thereon and other features described above may all bemodified for application to other derivative investment instruments,such as futures and options, within the purview and scope of the presentinvention. An advantage of the disclosed methods and derivativeinvestment instruments is that more traders at the exchange may havemore opportunity to trade new products and obtain new and valuablemarket information, thus increasing visibility of orders and thedesirability of maintaining a presence at the exchange.

The matter set forth in the foregoing description, accompanying drawingsand claims is offered by way of illustration only and not as alimitation. While particular embodiments have been shown and described,it will be apparent to those skilled in the art that changes andmodifications may be made without departing from the broader aspects ofapplicants' contribution. It is therefore intended that the foregoingdetailed description be regarded as illustrative rather than limiting,and that it be understood that it is the following claims, including allequivalents, that are intended to define the scope of this invention.

1. A non-transitory computer-readable medium containing processorexecutable program instructions for creating a volatility benchmarkindex, the instructions configured for causing a processor to executethe steps of: storing a value of a Treasury bill account less amark-to-market value of at least one of a volatility-based future oroption in a memory; calculating a value reflecting a volatilitybenchmark on the processor based on the stored value; and wherein thevalue reflecting a volatility benchmark is calculated according to theformula:VPD _(t) =M _(t)=(1+r _(t−1))VPD _(t−1)−M_(ult) N _(last)(f _(t) −f_(t−1)) where VPD_(t) is a VIX premium index value at date t, M_(t) is aTreasury bill balance on date t, r_(t−1) is an effective Treasury billrate from date t−1 to date t, N_(last) is a number of futures sold at alast roll date, F_(t) is a daily settlement price of futures at date t,and M_(ult) is a multiplier of the futures.
 2. The non-transitorycomputer-readable medium of claim 1, wherein on a roll date theprocessor executable program instructions are configured to cause theprocessor to calculate VPD_(t) according to the formula:VPD _(t)=(1+r _(t−1))VPD _(t−1) −M _(ult)(SOQ _(t) −F _(t−1))−N _(new)(F_(t) −F _(bid))) where SOQ_(t) is a final settlement price of theexpiring futures, N_(new) is the number of new futures and F_(bid) is anopening bid price of volatility-based futures.
 3. A non-transitorycomputer-readable medium containing processor executable programinstructions for creating a volatility benchmark index, the instructionsconfigured for causing a processor to execute the steps of: storing aclosing value of a Treasury bill account plus a mark-to-market value ofat least one of a volatility-based future or option in a memory;calculating a value reflecting a volatility benchmark on the processorbased on the stored closing value; and wherein the value reflecting avolatility benchmark is calculated according to the formula:VPD _(t) =M _(t)+100*10 N _(last) C _(t) where M_(t) is a Treasury billbalance at a close of date t, N_(last) is a number of futures sold and10 N_(last) is a number of volatility index (VIX) options bought at alast roll date, and C_(t) is an average of bid and ask quotes of VIXcalls at the close on date t.
 4. The non-transitory computer-readablemedium of claim 3, wherein the Treasury bill balance is calculated bycompounding a previous closing Treasury balance at a three-monthTreasury bill rate and netting a cash flow from VIX futures. 5.-8.(canceled)
 9. A method for creating a volatility benchmark index, themethod comprising: in a trading system having a memory and a processorin communication with the memory, the processor: storing in the memory avalue of a Treasury bill account less a mark-to-market value of at leastone of a volatility-based future or option in a memory; calculating avalue reflecting a volatility benchmark on the processor based on thestored value; and wherein the value reflecting a volatility benchmark iscalculated according to the formula:VPD _(t) =M _(t)=(1+r _(t−1))VPD _(t−1) −M _(ult) N _(last)(F _(t) −F_(t−1)) where VPD_(t) is a VIX premium index value at date t, M_(t) is aTreasury bill balance on date t, r_(t−1) is an effective Treasury billrate from date t−1 to date t, N_(last) is a number of futures sold at alast roll date, F_(t) is a daily settlement price of futures at date t,and M_(ult) is a multiplier of the futures.
 10. The method of claim 9,further comprising, on a roll date, the processor calculating VPD_(t)according to the formula:VPD _(t)=(1+r _(t−1))VPD _(t−1) −M _(ult)(SOQ _(t) −F _(t−1))−N _(new)(F_(t) −F _(bid))) where SOQ_(t) is a final settlement price of theexpiring futures, N_(new) is the number of new futures and F_(bid) is anopening bid price of volatility-based futures.